摘要
Practical experience has demonstrated that single objective functions, no matter how carefully chosen, prove to be inadequate in providing proper measurements for all of the characteristics of the observed data. One strategy to circumvent this problem is to define multiple fitting criteria that measure different aspects of system behavior, and to use multi-criteria optimization to identify non-dominated optimal solutions. Unfortunately, these analyses require running original simulation models thousands of times. As such, they demand prohibitively large computational budgets. As a result, surrogate models have been used in combination with a variety of multi- objective optimization algorithms to approximate the true Pareto-front within limited evaluations for the original model. In this study, multi-objective optimization based on surrogate modeling （multivariate adaptive regression splines, MARS） for a conceptual rainfall-runoff model （Xin＇anjiang model, XAJ） was proposed. Taking the Yanduhe basin of Three Gorges in the upper stream of the Yangtze River in China as a case study, three evaluation criteria were selected to quantify the goodness-of-fit of observations against calculated values from the simulation model. The three criteria chosen were the Nash-Sutcliffe efficiency coefficient, the relative error of peak flow, and runoff volume （REPF and RERV）. The efficacy of this method is demonstrated on the calibration of the XAJ model. Compared to the single objective optimization results, it was indicated that the multi-objective optimization method can infer the most probable parameter set. The results also demonstrate that the use of surrogate-modeling enables optimization that is much more efficient; and the total computational cost is reduced by about 92.5%, compared to optimization without using surrogate model- ing. The results obtained with the proposed method support the feasibility of applying parameter optimization to computationally intensive simulation models, via reducing the number of simulation runs required in the numerical model considerably.
Practical experience has demonstrated that single objective functions, no matter how carefully chosen, prove to be inadequate in providing proper measurements for all of the characteristics of the observed data. One strategy to circumvent this problem is to define multiple fitting criteria that measure different aspects of system behavior, and to use multi-criteria optimization to identify non-dominated optimal solutions. Unfortunately, these analyses require running original simulation models thousands of times. As such, they demand prohibitively large computational budgets. As a result, surrogate models have been used in combination with a variety of multi- objective optimization algorithms to approximate the true Pareto-front within limited evaluations for the original model. In this study, multi-objective optimization based on surrogate modeling （multivariate adaptive regression splines, MARS） for a conceptual rainfall-runoff model （Xin＇anjiang model, XAJ） was proposed. Taking the Yanduhe basin of Three Gorges in the upper stream of the Yangtze River in China as a case study, three evaluation criteria were selected to quantify the goodness-of-fit of observations against calculated values from the simulation model. The three criteria chosen were the Nash-Sutcliffe efficiency coefficient, the relative error of peak flow, and runoff volume （REPF and RERV）. The efficacy of this method is demonstrated on the calibration of the XAJ model. Compared to the single objective optimization results, it was indicated that the multi-objective optimization method can infer the most probable parameter set. The results also demonstrate that the use of surrogate-modeling enables optimization that is much more efficient; and the total computational cost is reduced by about 92.5%, compared to optimization without using surrogate model- ing. The results obtained with the proposed method support the feasibility of applying parameter optimization to computationally intensive simulation models, via reducing the number of simulation runs required in the numerical model considerably.
基金
Acknowledgements The work was supported by the National Basic Research Program of China （No. 2010CB951103）, the National Natural Science Foundation of China （Grant Nos. 41330854, 41371063 and 51309155） and the National Science ＆ Technology Pillar Program during the 12th Five-year Plan Period （2012BAC21B01 and 2012BAC19B03）. We are also thankful to anonymous reviewers and editors for their helpful comments and suggestions.
